By James Rodgers
BBC Moscow correspondent
The killing of Shamil Basayev will be a major boost for the Russian president.
In political terms, this is a big victory for the Russian leader, left
Moscow's most wanted man waged war on Russia for more than a decade.
"This is deserved retribution against the bandits for our children in Beslan, in Budennovsk, for all these acts of terror they committed in Moscow and other Russian regions," President Vladimir Putin said.
Basayev fought the Kremlin's troops. He boasted of planning attacks in which hundreds of civilians lost their lives.
Most notoriously, he said he was behind the hostage taking at a school in the southern Russian town of Beslan in 2004. More than 330 people, at least half of them children, were killed.
Shamil Basayev was a ruthless and bold enemy. Despite the very public and bloody nature of his attacks on Russian targets, and the price on his head, he evaded capture.
He even gave television interviews, embarrassing the agents who were hunting him.
Russia's security agency says Shamil Basayev was planning another attack to coincide with this weekend's G8 summit of world leaders in St Petersburg.
Instead, President Putin will be able to host the meeting knowing that Shamil Basayev is no longer a threat.
In political terms, especially in the Russian domestic arena, it is a big victory for the Russian leader.
Vyacheslav Nikonov, a political analyst close to the Kremlin, says it will also help Chechnya's pro-Moscow administration.
"On the whole, the situation has already been stabilised in many aspects, but the position of the regional leadership will strengthen even more after the killing of this notorious figure," he told the Interfax news agency.
Leaders loyal to the Kremlin had already been buoyed by the killing last month of Abdul-Khalim Saydullayev, who was regarded as 'president' among the rebels.
Moscow's public enemy number one, Basayev was a ruthless enemy
The conflict in Chechnya has calmed in comparison to the fierce fighting in the middle and at the end of the 1990s.
Separatist groups in the region have instead sought to spread the conflict beyond the borders of Chechnya itself.
The death of Shamil Basayev may well slow their advance. It is unlikely to halt it altogether.
Russia's North Caucasus regions are poor. Unemployment is high. As in other parts of the world, joining the ranks of Islamist militants is an option which appeals to some angry, frustrated, young men without work or prospects.
The Chechen fighters may have lost two leaders in as many months. It does not mean they are a spent force. Doku Umarov, who took over from Abdul-Khalim Saydullayev, is known to be close to Shamil Basayev.
During the past decade, the Kremlin has frequently claimed that the conflict in Chechnya was all but over - only for the fighting to flare up again.
The death of Shamil Basayev will deliver Moscow a big propaganda victory. It does not constitute a final victory over the forces who have fought the Kremlin's rule for more than 10 years.